Time/Tempo changes in clips

I play in a progressive metal band that's using Ableton Live to play backing tracks, and I'm looking for an easy way to keep Ableton's clock synced with our time signature and tempo changes. Tempo master/slave (https://www.ableton.com/en/manual/audio-clips-tempo-and-warping/#tempo-master-slave) seems to be close to what I'm looking for, but it still seems to only support a single tempo across the whole clip, and doesn't affect the time signature. Is there any way of embedding those changes within a clip, so that Live's clock will change automatically at the right time wherever I drop the backing track?

Right now we just have the metronome as a second backing track, and ignore Live's clock, but we're starting to do more with MIDI, so having accurate tempo/timing information is going to be necessary, and I'd rather not go through and insert all of the time signature changes (sometimes hundreds of them per set) manually every time I set up the project for a show.